Seminar: How much patience do you have ? Issues in complexity for nonlinear optimization

      Department of Systems Engineering and Engineering Management
                             The Chinese University of Hong Kong
Time: Friday (Feb 5th) 16:30pm- 17:30pm in ERB 513.
Title: How much patience do you have ? Issues in complexity for nonlinear
Speaker: Professor Philippe Toint, Department of Mathematics, The
University of Namur
Abstract: We review the available results on the evaluation complexity of
algorithms using Lipschitz-continuous Hessians for the approximate solution
of nonlinear and potentially nonconvex optimization problems. Here,
evaluation complexity is a bound on the largest number of problem functions
(objective, constraints) and derivatives evaluations that are needed before
an approximate first-order critical point of the problem is guaranteed to
be found. We start by considering the unconstrained case and examine
classical methods (such as Newton's method) and the more recent ARC2
method, which we show is optimal under reasonable assumptions. We then turn
to constrained problems and analyze the case of convex constraints first,
showing that a suitable adaptation ARC2CC of the ARC2 approach also
possesses remarkable complexity properties. We finally extend the results
obtained in simpler settings to the general equality and inequality
constrained nonlinear optimization problem by constructing a suitable
ARC2GC algorithm whose evaluation complexity also exhibits the same
remarkable properties.
Short Bio: Philippe L. Toint received his Ph.D. in 1978 under the guidance
of Prof M.J.D. Powell in University of Cambridge. He was appointed as
lecturer at the University of Namur in 1979 where he  became associate
professor in 1987 and full professor in 1993. Since 1979, he has been the
co-director of the Numerical Analysis Unit and director of the
Transportation Research Group in this department. He was in charge of the
University Computer Services from 1998 to 2000 and director of the
Department of Mathematics from 2006 to 2009. He currently serves as
Vice-rector for Research and IT for the university. His research interests
include numerical optimization, numerical analysis and transportation
research. He has published four books and more than 280 papers and
technical reports. He was elected as SIAM Fellow (2009), he was also
awarded the Beale-Orchard-Hayes Prize (1994, with Conn and Gould)) and the
Lagrange Prize in Continuous Optimization (2006, with Fletcher and
Leyffer). He is the past Chairman (2010-2013) of the Mathematical
Programming Society.
The talk is hosted by  Professor Shiqian Ma
Assistant Professor
Department of Systems Engineering and Engineering Management
The Chinese University of Hong Kong
Tel: +(852)39438240
Friday, February 5, 2016 - 08:30 to 09:30